Energy-Efficient Network Coding for the Noisy Channel Network

We investigate energy-efficient network coding with a bit error probability (BEP) constraint. The network consists of statistically independent binary noisy channels. An error marking algorithm is used to calculate the number of erroneous bits in the sinks. Then we can accurately calculate the BEP in the sinks from the channel BEPs. For a given coding scheme, we formulate the optimal energy allocation problem. We show that the problem is convex for BPSK modulation. Then, we check the problem of the joint optimal network coding and energy allocation. A procedure is formulated to solve the problem. A pruning rule is suggested to reduce the search effort. Numerical results show the energy saving from the equal energy allocation and non-optimal coding